{"id":15185,"date":"2018-03-09T09:02:14","date_gmt":"2018-03-09T09:02:14","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/curvas-hiperela%c2%adpticas-modulares\/"},"modified":"2018-03-09T09:02:14","modified_gmt":"2018-03-09T09:02:14","slug":"curvas-hiperela%c2%adpticas-modulares","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/curvas-hiperela%c2%adpticas-modulares\/","title":{"rendered":"Curvas hiperel\u00edpticas modulares"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Enrique Gonz\u00e1lez Jim\u00e9nez <\/strong><\/h2>\n<p>Una vez demostrada la conjetura de shimura-taniyana-weil, parece natural determinar otras familias de curvas definidas sobre q que sean modulares, entendida la modularidad de una curva como la propiedad de admitir un recubrimiento definido sobre q desde alguna curva modular x1(n).  el estudio de curvas de g\u00e9nero mayor que uno definidas sobre q que son modulares presenta diferencias notables respecto del caso de curvas el\u00edpticas definidas  sobre q. Por este motivo, introducimos la noci\u00f3n de curva modular nueva de nivel n. Tales curvas son aquellas para las cuales los correspondiente morfismos entre las jacobinas factorizan a trav\u00e9s de la parte nueva de la jacobiana de x1(n).  el principal resultado te\u00f3rico de esta tesis es el que establece que el conjunto de las curvas hiperel\u00edpticas modulares nuevas, salvo q-isomorfismo, es finito. Tras haber obtenido este inesperado resultado, nuestro objetivo se ha encaminado en la determinaci\u00f3n de estas curvas, es decir, a encontrar ecuaciones  y los correspondientes morfismos que las hacen modulares. Para ello, hemos acotado sus g\u00e9neros y encontrado condiciones sobre los niveles correspondientes. Creando paquetes computacionales, que recog\u00edan los resultados te\u00f3ricos demostrados, y utilizando propiedades de las curvas modulares y de las curvas hiperel\u00edpticas, hemos conseguido probar que solamente existen 213 de tales curvas con g\u00e9nero mayor que dos, hemos calculado 75 de tales curvas y presentamos evidencias num\u00e9ricas que sugieren que estas 288 curvas son todas las curvas hiperel\u00edpticas modulares nuevas, salvo q-isomorfismo.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Curvas hiperel\u00edpticas modulares<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Curvas hiperel\u00edpticas modulares <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Enrique Gonz\u00e1lez Jim\u00e9nez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 18\/01\/2002<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Josep Gonz\u00e1lez Rovira<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: enrique Nart vi\u00f1als <\/li>\n<li>adolfo Quiros gracian (vocal)<\/li>\n<li>pilar Bayer isant (vocal)<\/li>\n<li>john Cremona (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Enrique Gonz\u00e1lez Jim\u00e9nez Una vez demostrada la conjetura de shimura-taniyana-weil, parece natural determinar otras familias de curvas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[126,29903,14514],"tags":[29907,48551,37552,48553,48552,11720],"class_list":["post-15185","post","type-post","status-publish","format-standard","hentry","category-matematicas","category-teoria-algebraica-de-los-numeros","category-teoria-de-los-numeros","tag-adolfo-quiros-gracian","tag-enrique-gonzalez-jimenez","tag-enrique-nart-vinals","tag-john-cremona","tag-josep-gonzalez-rovira","tag-pilar-bayer-isant"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/15185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=15185"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/15185\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=15185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=15185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=15185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}